How to warp flat svg image
After importing a .SVG like this you see that it consists of many curves. 

You can convert it with Alt-C Mesh from Curve...

After scaling and rotating all elements and relocating some parts you should have something like that:


Then it is up to you to:


Animate the tree segments with glitter balls parented by simply keyframe their rotation.
Join all to one mesh and add a shape keys to animate them (use proportional editing)
Creating a rig is also possible but would be kinda overkill